Simplify the following expression: $\dfrac{144r^4}{96r^4}$ You can assume $r \neq 0$.
Explanation: $ \dfrac{144r^4}{96r^4} = \dfrac{144}{96} \cdot \dfrac{r^4}{r^4} $ To simplify $\frac{144}{96}$ , find the greatest common factor (GCD) of $144$ and $96$ $144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(144, 96) = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 = 48 $ $ \dfrac{144}{96} \cdot \dfrac{r^4}{r^4} = \dfrac{48 \cdot 3}{48 \cdot 2} \cdot \dfrac{r^4}{r^4} $ $\phantom{ \dfrac{144}{96} \cdot \dfrac{4}{4}} = \dfrac{3}{2} \cdot \dfrac{r^4}{r^4} $ $ \dfrac{r^4}{r^4} = \dfrac{r \cdot r \cdot r \cdot r}{r \cdot r \cdot r \cdot r} = 1 $ $ \dfrac{3}{2} \cdot 1 = \dfrac{3}{2} $